Operator Dynamics Approach to Short-Arc Orbital Prediction Based on the Wigner Distribution

We propose an uncertainty propagation framework based on phase space that treats the error distribution as the marginal of a Wigner quasi-probability distribution and defines an effective uncertainty constant quantifying the minimal resolvable phase-space cell. Recognizing that observational updates systematically reduce uncertainty, we adopt a generalized Koopman–von Neumann equation grounded in operator dynamical modeling to propagate the density operator corresponding to the error distribution. The scaling parameter κ quantifies the reduction in uncertainty following each filter update. Although the potential is presently retained only to second order—so that both propagation and update preserve Gaussian form and permit direct Kalman recursion—the framework itself lays the analytical foundation for a future treatment of non-Gaussian features. Validated on 1215 orbits (semi-major axis: 9600 km to 42,164 km), the method shows that within a 3 min fit/10 min forecast window, observational noise contributes 350 m while unmodeled dynamics adds only 0.6 m. Kruskal–Wallis rank-sum tests and the accompanying scatter-plot trend rank the semi-major axis as the dominant sensitive parameter. The proposed model outperforms Chebyshev and high-fidelity propagators in real time, offering a physically interpretable route for short-arc orbit prediction.